Design Of Statistical Distribution Modeling Method For High Precision Timing Analysis

The continuous development of the integrated circuit industry and the industry’s continuous pursuit of high energy efficiency have made the technology node continuely shrink and the operating voltage continuely drop.As the operating voltage of the circuit decreases,the influence of process parameters on the circuit delay gradually changes from linear to nonlinear,which in turn causes the circuit delay distribution to exhibit a Non-Gaussian distribution.At the same time,the reduction in technology node makes the variation of process parameters more significant,which causes the Non-Gaussian phenomenon of the circuit delay distribution at low voltage to be more serious,which makes the traditional corner-based deterministic timing analysis method too pessimistic.Although the statistical timing analysis method can better analyze the effect of process parameter variations in advanced technology nodes,it still exists following two problems in low-voltage scenarios: First,due to the obvious NonGaussian distribution of cell delays at low voltages,it is difficult to establish a high-precision model between process parameters and delays.Second,due to the large error of the cell delay models,it is difficult to meet the accuracy requirements for the timing analysis of large-scale circuits at low voltages.The work of this thesis first studies three methods for cell delay modeling,and selects multiple adaptive regression spline method as the basic modeling method to be optimized.Aiming at the significant accuracy problem due to the influence of key parameters when using the MARS method for cell delay modeling,a strategy is used to combine the particle swarm optimization algorithm with MARS to search for the optimal parameters of the model,so the PSO-MARS cell delay model is gotten.Secondly,the MARS method in this work is further used to model the path delay.A combination of canonical correlation analysis and MARS method is proposed for the problem of the long model fitting time when using MARS method for path delay modeling.It firstly extracts the critical process parameters of the path through cannonical correlation analysis.Then the path delay model is built by using the critical process parameters and the CCA-MARS path delay model is gotten.In this work,multiple combinational logic cells and ISCAS85 benchmark circuits is used under SMIC 28 nm to verify the effectiveness of the modeling and optimization of cells and paths.The results show that at 0.8V and0.6V,the average error of-3σ delay point of the PSO-MARS cell delay model are 0.24% and 1.31% compared with Monte Carlo simulation results,while the average error of +3σ delay point are 0.45% and 0.83% compared with the original one.These errors are reduced by 33.33% and 47.28%,26.23% and 65.82%,respectively.Compared with the original path delay MARS model,the average errors of-3σ delay point of optimized model are reduced by 53.06%and 78.47%.The average errors of +3σ delay point are reduced by 8.33% and 28.61% and the average fitting time of the model are shortened by 90.76% and 94.11%,so that the high precision statistical timing analysis of the path is achieved.